Question

A laser beam is of 9 mW, diameter = 2 mm. Then
what is the amplitude of magnetic field associated
with it?
(1) 49 ut
(2) 98 uT
(3) 9.8 uT
(4) 4.9 uT
m​

Answer 1

Thus the amplitude of magnetic field is B = 4.9  μT

Option (D) is correct.

Explanation:

We have the following equation and calculations:

S = P / A= cε0 E(rms) ^2

E(rms)  =  √ P / Acϵo

E(rms)  =   √0.009 / π x (10^-3) x ( 3 x 10^8) x (8.85 x 10^12)

E(rms)  = 1038.7 V/m

B(rms)  = E(rms)/c

B(rms)  = 1038.7 / 3 x 10^8

B(rms)  = 3.46 μT

B = √2 B rms

B = 4.9  μT

Thus the amplitude of magnetic field is B = 4.9  μT

 

​

Answer 2

The amplitude of magnetic field associated  with it is (4) 4.9 μT

Explanation:

The amplitude A is given by the formula:

S = P/A

S = cε₀Erms²

P/A = cε₀Erms²

Erms = √(P/Acε₀)

On substituting the values, we get,

Erms = √(0.009/(π × (10⁻³) × (3 × 10⁸) × (8.85 × 10¹²)))

∴ Erms = 1038.7 V/m

Now, the magnetic field is given by the formula:

Brms = Erms/c

On substituting the values, we get,

Brms = 1038.7/(3 × 10⁸)

∴ Brms = 3.46 μT

B = √2 Brms

B = √2 × 3.46 μ

∴ B = 4.9 μT